Geodesic
Destruction of solutions of wave equations in systems with distributed parameters
Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 2, pp. 206-213 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider two initial boundary value problems on an interval with homogeneous Dirichlet conditions. These problems were proposed by M. I. Rabinovich and D. I. Trubetskov and are given by nonlinear fourth-order Sobolev-type equations. We prove the local-in-time existence of a strong generalized solution of one problem, and for both problems, we obtain sufficient conditions for the destruction of their strong generalized solutions in a finite time.
Mots-clés : destruction
Keywords: nonlinear analysis. 
@article{TMF_2011_167_2_a3,
     author = {M. O. Korpusov},
     title = {Destruction of solutions of wave equations in systems with distributed parameters},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {206--213},
     year = {2011},
     volume = {167},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_167_2_a3/}
}
TY  - JOUR
AU  - M. O. Korpusov
TI  - Destruction of solutions of wave equations in systems with distributed parameters
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2011
SP  - 206
EP  - 213
VL  - 167
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2011_167_2_a3/
LA  - ru
ID  - TMF_2011_167_2_a3
ER  - 
%0 Journal Article
%A M. O. Korpusov
%T Destruction of solutions of wave equations in systems with distributed parameters
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2011
%P 206-213
%V 167
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2011_167_2_a3/
%G ru
%F TMF_2011_167_2_a3
M. O. Korpusov. Destruction of solutions of wave equations in systems with distributed parameters. Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 2, pp. 206-213. http://geodesic.mathdoc.fr/item/TMF_2011_167_2_a3/

[1] M. I. Rabinovich, Izv. vuzov. Radiofiz., 17:4 (1974), 477–510 | MR

[2] M. I. Rabinovich, D. I. Trubetskov, Vvedenie v teoriyu kolebanii i voln, Nauka, M., 1984

[3] E. L. Mitidieri, S. I. Pokhozhaev, Apriornye otsenki i otsutstvie reshenii nelineinykh uravnenii i neravenstv v chastnykh proizvodnykh, Tr. MIAN, 234, eds. S. M. Nikolskii, E. F. Mischenko, Nauka, M., 2001 | MR | Zbl

[4] H. A. Levine, Arch. Ration. Mech. Anal., 51:5 (1973), 371–386 | DOI | MR | Zbl

[5] H. A. Levine, P. Pucci, J. Serrin, “Some remarks on global nonexistence for nonautonomous abstract evolution equations”, Harmonic Analysis and Nonlinear Differential Eequations, Contemp. Math., 208, eds. M. L. Lapidus, L. H. Harper, A. J. Rumbos, AMS, Providence, RI, 1997, 253–263 | DOI | MR | Zbl

[6] A. A. Samarskii, V. A. Galaktionov, S. P. Kurdyumov, A. P. Mikhailov, Rezhimy s obostreniem v zadachakh dlya kvazilineinykh parabolicheskikh uravnenii, Nauka, M., 1987 | MR | Zbl

[7] V. A. Galaktionov, S. I. Pokhozhaev, Zh. vychisl. matem. i matem. fiz., 48:10 (2008), 1819–1846 | DOI | MR | Zbl

[8] A. G. Sveshnikov, A. G. Alshin, M. O. Korpusov, Yu. D. Pletner, Lineinye i nelineinye uravneniya sobolevskogo tipa, Fizmatlit, M., 2007 | Zbl

[9] M. O. Korpusov, Razrushenie v neklassicheskikh volnovykh uravneniyakh, URSS, M., 2010

[10] M. O. Korpusov, Razrushenie v neklassicheskikh nelokalnykh uravneniyakh, URSS, M., 2011